Class 11 Mathematics Statistics MCQs

Question : The observations 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95 are arranged in ascending order. What is the value of x if the median of the data is 63? 
(a) 61
(b) 62
(c) 62.5
(d) 63

Answer : B

Question : The mode of the given distribution is: 
Weight (in kg)               40    43    46   49   52   55
Number of children       5     8     16      9     7    3
(a) 40
(b) 55
(c) 49
(d) 46

Answer : D

Question : Find the median of 18, 35, 10, 42, 21 
(a) 20
(b) 19
(c) 21
(d) 22

Answer : C

Question : While dividing each entry in a data by a nonzero number a, the arithmetic mean of the new data: 
(a) is multiplied by a
(b) does not change
(c) is divided by a
(d) is diminished by a

Answer : C

Question : The standard deviation of 7, 9, 11, 13, 15 is: 
(a) 2.82
(b) 2.4
(c) 2.7
(d) 2.5

Answer : A

Question : The mean of six numbers is 30. If one number is excluded, the mean of the remaining numbers is 29. The excluded number is 
(a) 29
(b) 30
(c) 35
(d) 45

Answer : C

Question : The mean of a set of 20 observation is 19.3. The mean is reduced by 0.5 when a new observation is added to the set. The new observation is 
(a) 19.8
(b) 8.8
(c) 9.5
(d) 30.8

Answer : B

Question : Consider the first 10 positive integers. If we multiply each number by –1 and then add 1 to each number, the variance of the numbers so obtained is 
(a) 8.25 "
(b) 6.5
(c) 3.87
(d) 2.87

Answer : A

Question : The algebraic sum of the deviations of 20 observations measured from 30 to 20. What is the value of the mean of the observations ? 
(a) 30
(b) 30.1
(c) 29
(d) 31

Answer : D

Question : The mean deviation from the median of the following set of observations 5, 3, 9, 12, 3, 10, 12, 21, 18, 12, 21 is 
(a) 5.113
(b) 4.606
(c) 4.134
(d) 4.909

Answer : D

Question : The median from the table 
value                7   8   9   10   11   12   13
frequency is:  2   1   5      4     6     1    3
(a) 100
(b) 10
(c) 110
(d) 1110

Answer : B

Question : The coefficient of variation from the given data class 0-10 10-20 20-30 30-40 40-50 interval frequency 2 10 8 4 6 is : 
(a) 50
(b) 51.9
(c) 48
(d) 51.8

Answer : C

Question : The average of 5 quantities is 6, the average of three of them is 4, then the average of remaining two numbers is : 
(a) 9
(b) 6
(c) 10
(d) 5

Answer : A

Question : The mode of the following series 3, 4, 2, 1, 7, 6, 7,6, 8, 6, 5 is 
(a) 5
(b) 6
(c) 7
(d) 8

Answer : B

Question : The co-efficient of variation is computed by: 
(a) mean/ standard deviation
(b) standard deviation /mean
(c) mean /standard deviation x 100
(d) standard deviation / mean x 100

Answer : D

Question : What is the standard deviation of the following series ? 
Measurements 0 -10   10 - 20    20 -30   30 - 40
Frequency           1          3             4           2
(a) 81
(b) 7.6
(c) 9
(d) 2.26

Answer : C

Question : The mean deviation from the mean of the following data : 
Marks   0-10    10-20    20-30    30-40   40-50
No. of     5            8         15         16         6
Students
is
(a) 10
(b) 10.22
(c) 9.86
(d) 9.44

Answer : D

Question : The standard deviation for the following data is 
Wages per week upto  15   30   45    60     75     90     105    120
Number of Workers      12   30   65   107   157    202    222   230
(a) 26.75
(b) 24.46
(c) 25.89
(d) none

Answer : C

Question : The mean of 13 observations is 14. If the mean of the first 7 observations is 12 and that of the last 7 observations is 16, what is the value of the 7th observation ? 
(a) 12
(b) 13
(c) 14
(d) 15

Answer : C

Question : A batsman scores runs in 10 innings 38, 70, 48,34, 42, 55, 63, 46, 54 and 44, then the mean deviation is 
(a) 8.6
(b) 6.4
(c) 10.6
(d) 9.6

Answer : A

Question : Let x₁, x_2, .....xn be n observations. Let wi = l xi + k for i = 1, 2, ... n, where l and k are constants. If the mean of xi’s is 48 and their standard deviation is 12, the mean of w’is is 55 and standard deviation of w’is is 15, the values of l and k should be 
(a) l = 1.25, k = – 5
(b) l = –1.25, k = 5
(c) l = 2.5, k = – 5
(d) l = 2.5, k = 5

Answer : A

Question : Standard deviations for first 10 natural numbers is 
(a) 5.5
(b) 3.87
(c) 2.97
(d) 2.87

Answer : D

Question : The standard deviation of some temperature data in °C is 5. If the data were converted into °F, the variance would be 
(a) 81
(b) 57
(c) 36
(d) 25

Answer : A

Question : The variance of the following distribution is 
x₁ 2 3 11
f(x₁) 1/3 1/2 1/6
(a) 10
(b) 16
(c) 8
(d) 7.5

Answer : A

Question : In an experiment with 15 observations on x, the following results were available :Sx2 = 2830, Sx =170One observation that was 20 was found to be wrong and was replaced by the correct value 30. The corrected variance is 
(a) 8.33
(b) 78.00
(c) 188.66
(d) 177.33

Answer : B

Question : In a series of 2 n observations, half of them equal a and remaining half equal –a. If the standard deviation of the observations is 2, then |a| equals. 
(a) √2 / n
(b) √2
(c) 2 
(d) 1/n

Answer : C

Question : A scientist is weighing each of 30 fishes. Their mean weight worked out is 30 gm and a standarion deviation of 2 gm. Later, it was found that the measuring scale was misaligned and always under reported every fish weight by 2 gm. The correct mean and standard deviation (in gm) of fishes are respectively : 
(a) 32, 2
(b) 32, 4
(c) 28,2
(d) 28, 4

Answer : A

Question : In a batch of 15 students, if the marks of 10 students who passed are 70, 50, 95, 40, 60, 70, 80, 90, 75, 80 then the median marks of all the 15 students is: 
(a) 40
(b) 50
(c) 60
(d) 70

Answer : C

Question : If f (x + y, x – y) = xy, then the arithmetic mean of f (x, y) and f(y, x) is : 
(a) x
(b) y
(c) 0
(d) none of these

Answer : C

Question : If a variable takes discrete values x + 4, x - 7/2 , x - 5/2 , x - 3 , x - 2 , x + 1/2 , x - 1/2 , x + 5 (x is positive), then the median is : 
(a) x - 5/4
(b) x - 1/2
(c) x - 2 
(d) x + 5/4

Answer : A

Question : If the mean deviation of the numbers 1, 1 + d, ..., 1 + 100d from their mean is 255, then a value of d is :
(a) 10.1
(b) 5.05
(c) 20.2
(d) 10
Answer : A

Question : Mean of 5 observations is 7. If four of these observations are 6, 7, 8, 10 and one is missing then the variance of all the five observations is :
(a) 4
(b) 6
(c) 8
(d) 2
Answer : D

Question : Let x , M and s² be respectively the mean, mode and variance of n observations x₁, x₂, ...., xn and d_i = – x_i – a , i = 1, 2, ...., n, where a is any number.
Statement I: Variance of d₁, d₂,... dn is σ^₂.
Statement II: Mean and mode of d₁, d₂, .... dn are -x - a and – M – a, respectively. 
(a) Statement I and Statement II are both false
(b) Statement I and Statement II are both true
(c) Statement I is true and Statement II is false
(d) Statement I is false and Statement II is true
Answer : B

Question : A scientist is weighing each of 30 fishes. Their mean weight worked out is 30 gm and a standarion deviation of 2 gm. Later, it was found that the measuring scale was misaligned and always under reported every fish weight by 2 gm. The correct mean and standard deviation (in gm) of fishes are respectively :
(a) 32, 2
(b) 32, 4
(c) 28, 2
(d) 28, 4
Answer : A

Question : All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given ? 
(a) mean
(b) median
(c) mode
(d) variance
Answer : D

Question : Let x₁ , x₂,...., xn be n observations, and let x be their arithmetic mean and σ² be the variance.
Statement-1 : Variance of 2x₁, 2x₂, ..., 2x_n is 4σ².
Statement-2 : Arithmetic mean 2x₁, 2x₂, ..., 2x_n is 4 x .
(a) Statement-1 is false, Statement-2 is true.
(b) Statement-1 is true, statement-2 is true; statement-2 is a correct explanation for Statement-1.
(c) Statement-1 is true, statement-2 is true; statement-2 is not a correct explanation for Statement-1.
(d) Statement-1 is true, statement-2 is false.
Answer : D

Question : For two data sets, each of si e 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is
(a) 11/2
(b) 6
(c) 13/2
(d) 5/2
Answer : A

Question : If the mean of 4, 7, 2, 8, 6 and a is 7, then the mean deviation from the median of these observations is
(a) 8
(b) 5
(c) 1
(d) 3
Answer : D

Question : If mean and standard deviation of 5 observations x₁, x₂, x₃, x₄, x₅ are 10 and 3, respectively, then the variance of 6 observations x₁, x₂, ..., x₅ and – 50 is equal to:
(a) 509.5
(b) 586.5
(c) 582.5
(d) 507.5
Answer : D

Question : If the mean of the data : 7, 8, 9, 7, 8, 7, l, 8 is 8, then the variance of this data is
(a) 9/8
(b) 2
(c) 7/8
(d) 1
Answer : D

Question : If the mean deviation about the median of the numbers a, 2a,.......,50a is 50, then | a | equals 
(a) 3
(b) 4
(c) 5
(d) 2
Answer : B

Question : Statement-1 : The variance of first n even natural numbers is n² –1/4.
Statement-2 : The sum of first n natural numbers is n(n + 1) /2 and the sum of squares of first n natural numbers is n (n + 1)(2n + 1)/6.
(a) Statement-1 is true, Statement-2 is true. Statement-2 is not a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is false.
(c) Statement-1 is false, Statement-2 is true.
(d) Statement-1 is true, Statement-2 is true. Statement-2 is a correct explanation for Statement-1.
Answer : C

Question : In a set of 2n observations, half of them are equal to 'a' and the remaining half are equal to ' –a'. If the standard deviation of all the observations is 2 ; then the value of | a | is :
(a) 2
(b) √2
(c) 4
(d) 2√2
Answer : A

Question : The sum of 100 observations and the sum of their squares are 400 and 2475, respectively. Later on, three observations, 3, 4 and 5, were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is :
(a) 8.25
(b) 8.50
(c) 8.00
(d) 9.00
Answer : D

Question : The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?
(a) a = 0, b = 7
(b) a = 5, b = 2
(c) a = 1, b = 6
(d) a = 3, b = 4
Answer : D

Question : The mean and the standard deviation (s.d.) of five observations are 9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is?
(a) 0
(b) 4
(c) 2
(d) 1
Answer : C

Question : Suppose a population A has 100 observations 101, 102, ............., 200 and another population B has 100 obsevrations 151, 152, ................ 250. If V_A and V_B represent the variances of the two populations, respectively then VA/VB is
(a) 1
(b) 4/9
(c) 9/4
(d) 3/2
Answer : A

Question : In an experiment with 15 observations on x, the following results were available:
∑x² = 2830, Sx = 170
One observation that was 20 was found to be wrong and was replaced by the correct value 30. The corrected variance is 
(a) 8.33
(b) 78.00
(c) 188.66
(d) 177.33
Answer : B

Question : The median of 19 observations is 30. Two more observations are made and the values of these are 8 and 32. The median of the 21 observations taken together is equal to: 
(a) 28
(b) 30
(c) 32
(d) 34

Answer : B

Question : If in a frequency distribution table with 12 classes, the width of each class is 2.5 and the lowest class boundary is 6.1, then what is the upper class boundary of the highest class? 
(a) 30.1
(b) 27.6
(c) 30.6
(d) 36.1

Answer : D

Question : The outcome of each of 30 items was observed; 10 items gave an outcome 1/2 - d each, 10 items gave outcome 1/2 each and the remaining 10 items gave outcome 1/2 + d each. If the variance of this outcome data is 4/3 then |d| equals :
(a) 2/3
(b) 2
(c) 5/2
(d) 2
Answer : D

Question : Let X and M.D. be the mean and the mean deviation about X of n observations xi, i = 1, 2, ........, n. If each of the observations is increased by 5, then the new mean and the mean deviation about the new mean, respectively, are:
(a) X,M.D.
(b) X + 5,M.D.
(c) X,M.D.+ 5
(d) X + 5,M.D.+ 5
Answer : B

Question : If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?
(a) 3a² – 34a + 91 = 0
(b) 3a² – 23a + 44 = 0
(c) 3a² – 26a + 55 = 0
(d) 3a² – 32a + 84 = 0
Answer : D

Question : In a series of 2 n observations, half of them equal a and remaining half equal –a. If the standard deviation of the observations is 2, then |a| equals.
(a) √2/n
(b) √2
(c) 2
(d) 1/n
Answer : C

Question : The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is:
(a) 10 : 3
(b) 4 : 9
(c) 5 : 8
(d) 6 : 7
Answer : B

Question : The variance of first 50 even natural numbers is
(a) 437
(b) 437/4
(c) 833/4
(d) 833
Answer : D

Question : 5 students of a class have an average height 150 cm and variance 18 cm2. A new student, whose height is 156 cm, oined them. The variance (in cm2) of the height of these six students is:
(a) 16
(b) 22
(c) 20
(d) 18
Answer : C

Question : Consider the following statements :
(A) Mode can be computed from histogram
(B) Median is not independent of change of scale
(C) Variance is independent of change of origin and scale.
Which of these is / are correct ?
(a) (A), (B) and (C)
(b) Only (B)
(c) Only (A) and (B)
(d) Only (A)
Answer : C

Question : The mean of 5 observations is 5 and their variance is 124.
If three of the observations are 1, 2 and 6; then the mean deviation from the mean of the data is :
(a) 2.5
(b) 2.6
(c) 2.8
(d) 2.4
Answer : C

Question : If the mean deviation of the numbers 1, 1 + d, 1 + 2d, .... 1 + 100d from their mean is 255, then d is equal to:
(a) 20.0
(b) 10.1
(c) 20.2
(d) 10.0
Answer : B

Question : Statement 1: The variance of first n odd natural numbers is n² - 1 / 3
Statement 2: The sum of first n odd natural number is n² and the sum of square of first n odd natural numbers is n( n² + 1) / 3.
(a) Statement 1 is true, Statement 2 is false.
(b) Statement 1 is true, Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.
(c) Statement 1 is false, Statement 2 is true.
(d) Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
Answer : A